(CNN) -- A man who local police believe was responsible for a fatal car bombing in Ciudad Juarez, Mexico, is in custody, a municipal police spokesman told CNN Sunday.

But federal police, while confirming that the man is in custody after a shootout with the Mexican military, said they had nothing linking him to the bombing.

The July 15 car bombing claimed the lives of two police officers and a paramedic. Six people were injured in the blast.

Carlos Vasquez Barragan, a suspected leader of La Linea -- the armed wing of the Juarez drug cartel -- was detained after a shootout with the Mexican military on Thursday near the city of Madera, police spokesman Jacinto Seguro told CNN.

"During that shootout, which included the use of heavy arms, grenades, dynamite and AK-47s, the military captured him," Seguro said.

Seguro did not elaborate Sunday on why municipal police believe Vasquez Barragan is responsible for the July 15 car bombing, or what evidence authorities have in that case.

While Seguro was insistent Sunday that municipal police believe Vasquez Barragan was responsible for the car bombing, federal police spokesman Ramon Salinas said he was unaware of any definite connection.

"He has nothing to do with the car bombing that we know of for sure," Salinas said.

Salinas confirmed Vasquez Barragan, 39, was in custody and that federal authorities consider him a kingpin in the Juarez cartel, holding one of the highest positions in the cartel's leadership structure. According to Salinas, he is the leader of La Linea's hit men.

Meanwhile, the mayor of Juarez, Jose Reyes Ferriz, said in an e-mail to CNN that Vasquez Barragan may have had a small part in the bombing, but it was still unclear.

Shortly after the car bomb incident, Seguro described it as an attempt to draw police officers to the area where the car bomb was set.

He said that federal police were responding to a call that a police officer had been killed.

"When they went to check the car, there was a dead body in there, dressed up like a police officer, but it wasn't one of ours," Seguro said. "They [whoever set the bomb] put him in a civilian car but dressed him up in a municipal police uniform. That's when the bomb went off. It's like an act of terrorism."

In the confrontation in which Vasquez Barragan was captured, eight suspected drug traffickers were killed, federal police spokesman Salinas said.

"A group of about 100 soldiers were on patrol in the mountainous area near Madera, northwest of Chihuahua when they were fired upon by a group of armed gunmen. Eight of the bad guys were killed in the shootout. The Mexican military did not suffer any casualties," Salinas said.

The area where the conflict happened is a major drug-trafficking corridor, Salinas said.